This is not a bug. It was decided early on that / for two integers in Julia should produce a floating-point value. If you want a Rational result, use Rational inputs.
It might be interesting to have a library for exact linear-algebra calculations on integer matrices, perhaps along the lines of LinBox. But since the algorithms appear to be quite different, it seems like it should be a separate package from “ordinary” generic linear algebra routines that rely on division.